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I just can't get this number out of my head. It's a number that has the decimal digits composed by all the prime numbers.

The first digit is not important, it can be 0,2357... or 1,2357...

Does any mathematician has studied this number? Is it transcendental? I guess I can prove it's not a normal number. Where can I find more about it?

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  • $\begingroup$ 1 isn't a prime number $\endgroup$
    – JMP
    Commented Apr 18, 2017 at 13:57
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    $\begingroup$ smarandache studies this sort of thing $\endgroup$
    – JMP
    Commented Apr 18, 2017 at 13:57
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    $\begingroup$ The number is called Copeland–Erdős constant, and it has been studied before. $\endgroup$
    – Loreno Heer
    Commented Apr 18, 2017 at 14:04
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    $\begingroup$ and it is a normal number by the way $\endgroup$
    – Loreno Heer
    Commented Apr 18, 2017 at 14:05
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    $\begingroup$ Most primes have over a billion digits, so neither the first digit nor the last digit has much of an effect, and asymptotically the first and last digits have no effect. $\endgroup$
    – Douglas Zare
    Commented Apr 19, 2017 at 23:08

1 Answer 1

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The Copeland–Erdős constant is the concatenation of "0." with the base 10 representations of the prime numbers in order. Its value is approximately 0.235711131719232931374143… (sequence A033308 in the OEIS).

In base 10, the constant is a normal number, a fact proven by Arthur Herbert Copeland and Paul Erdős in 1946 (hence the name of the constant).

https://en.wikipedia.org/wiki/Copeland%E2%80%93Erd%C5%91s_constant

thx to Loreno Heer

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